The expression which represents a whole number which is the preceding number to a whole number x is; x-1.
What are whole numbers?Whole numbers are a class of numbers which are otherwise termed, Integers. Furthermore, Integers number values include, 1, 5 and -3 among a host of other numbers.
Hence, if the actual number is; x, then it follows that the number which precedes x is such that it is less than x by 1 unit.
Ultimately, the required preceding number is; x-1.
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Solve each proportion.
(z-1)/3 = 8/(z+1)
[tex]\dfrac{z-1}3 = \dfrac8{z+1}[/tex]
Eliminate the denominators.
[tex]3(z+1)\cdot\dfrac{z-1}3 = 3(z+1)\cdot\dfrac8{z+1}[/tex]
[tex]z^2 - 1 = 24[/tex]
Solve for [tex]z[/tex].
[tex]z^2 = 25[/tex]
[tex]\boxed{z = \pm5}[/tex]
About what percent of 9-ounce bags of this brand of potato chips weigh less than the advertised 9 ounces? Is this likely to pose a problem for the company that produces these chips?
Answer:
0.82%
Step-by-step explanation:
Question 6 of 10
Maureen has 5 rolls of pennies containing 50 coins each, 3 rolls of nickels
containing 40 coins each, 6 rolls of dimes containing 50 coins each, and 4
rolls of quarters containing 40 coins each. How much money does she have?
C A. $78.50
B. $83.50
C. $17.50
D. $8.30
Answer:
A $78.50
Step-by-step explanation:
Pennies $2.50
nickels $6.00
dimes $30.00
quarters $40.00
330/36
4 The students in an art class have blue cloth that is 60 inches long, gold cloth that is
48 inches long, and white cloth that is 72 inches long. They want to cut all the cloth
into pieces of equal length for a project.
What is the greatest possible length of the pieces without having any cloth left
over? Explain your reasoning.
How many pieces of each color cloth will they have?
If:
JL = 26,
KL=3x + 7, and
JK = 8x + 8,
Find KL.
J
K
L
Answer:
KL = 10
Step-by-step explanation:
Given:
[tex]JL=26[/tex]
[tex]KL=3x+7[/tex]
[tex]JK=8x+8[/tex]
From inspection of the given diagram:
[tex]JK+KL=JL[/tex]
Substitute the given values into the found equation and solve for x:
[tex]\implies 8x+8+3x+7=26[/tex]
[tex]\implies 11x+15=26[/tex]
[tex]\implies 11x+15-15=26-15[/tex]
[tex]\implies 11x=11[/tex]
[tex]\implies \dfrac{11x}{11}=\dfrac{11}{11}[/tex]
[tex]\implies x=1[/tex]
Substitute the found value of x into the expression for KL:
[tex]\implies KL=3(1)+7[/tex]
[tex]\implies KL=3+7[/tex]
[tex]\implies KL=10[/tex]
Formula we use,
→ JK + KL = JL
Now the value of x will be,
→ (8x + 8) + (3x + 7) = 26
→ 11x + 15 = 26
→ 11x = 26 - 15
→ x = 11/11
→ [ x = 1 ]
Then the value of KL will be,
→ 3x + 7
→ (3 × 1) + 7
→ 3 + 7 = 10
Hence, the value of KL is 10.
Compare the digits in the hundredths place of 4.241 and 4.25.
4 is less than 5, so 4.241 is less than 4.25.
Given the numbers are 4.241 and 4.25.
Because 4.241 and 4.25 have the same units and tenth digit (4.2 = 4.2)
so we need to compare the hundredths place that is, 0.041 with 0.05.
A decimal's distance from one whole increases as it increases in size. A decimal is further away from one whole the smaller it is. The amount of digits in each decimal should be your primary point of focus. Each of them contains two digits, allowing for immediate comparison.
The number following the decimal point is called the hundredths place. Round up the number of hundredths if the third number after the decimal is 5 or above. Keep the hundredths number constant if the number in the third position after the decimal point is 4 or less.
0.041 < 0.05
hence we get 4.241 < 4.25
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what could be possible ones digit of square.root of each of the following number 9801
The square root of 9801 is 99.
What is square root?√9801 = 99
A number can be obtained by multiplying the square root of that integer by itself.
The equation √y = √y12 can be used to express the square root of any number. In other words, if a number's exponent is 1/2, we must determine the number's square root.
The context of complex numbers can be used to discuss square roots of negative numbers. More broadly, square roots can be taken into account in any situation where the concept of an object's "square" is established. Among other mathematical structures, these include square matrices and function spaces.
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A plant splits into 3 new plants each week. How many plants will you have after 4 weeks?
Answer: You will have 12 plants in 4 weeks.
Step-by-step explanation: You will 12 plants because you get 3 new plants every week. So 4 weeks times 3 plants each week gives you 12 plants in 4 weeks.
the following dotplot shows the number of songs on each album in sal's collection. each dot represents a different album. 0022446688101012121414161618182020number of songs here is the five-number summary for these data: five-number summary min \text{q} 1q 1 start text, q, end text, start subscript, 1, end subscript median \text{q} 3q 3 start text, q, end text, start subscript, 3, end subscript max 444 999 101010 131313 202020 according to the 1.5\cdot \text{iqr}1.5⋅iqr1, point, 5, dot, start text, i, q, r, end text rule for outliers, how many low outliers are there in the data set? choose 1 answer: choose 1 answer:
There is only one value greater than 19, which is 20, indicating that the data set contains one high outlier.
What are a data set's median and quartiles?The data set's median, or 50th percentile, separates the bottom half from the upper half.The first quartile represents the median of the first half of the data set, which also represents the 25th percentile.The third quartile is the median of the data set's second half, which is also the 75th percentile.The inter-quartile range is the distance between the third and first quartiles.
Because the dot plot demonstrates the frequency of each inspection, the total data-set is given by:
4, 7, 8, 8, 9, 9, 10, 10, 10, 10, 11, 12, 12, 13, 13, 14, 16, 18, 20The following are the quartiles:
The first half is made up of the first nine elements, which are given by 4, 7, 8, 8, 9, 9, 10, 10, and thus Q1 = 9.The second half is made up of the last nine elements, which are 11, 12, 12, 13, 14, 16, 18, 20, and thus Q3 = 13.The IQR is calculated as follows:
IQR = Q3 - Q1 = 13 - 9 = 4The high outliers are values that are higher than 1.5 standard deviations above Q3, so the threshold is given by:
13 + 1.5 x 4 = 19Therefore, there is only one value greater than 19, which is 20, indicating that the data set contains one high outlier.
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The correct question is given below:
The following dot plot shows the number of songs on each album in Sal's collection. Each dot represents a different album.
A dot plot with an axis labeled "number of songs" and numbered from 0 to 20 in increments of 1, with 19 points. 4, frequency 1. 7, frequency 1. 8, frequency 2. 9, frequency 2. 10, frequency 4. 11, frequency 1. 12, frequency 2. 13, frequency 2. 14, frequency 1. 16, frequency 1. 18, frequency 1. 20, frequency 1.
Here is the five-number summary for these data:
Five-number summary
min \text{Q}_1Q
1
start text, Q, end text, start subscript, 1, end subscript median \text{Q}_3Q
3
start text, Q, end text, start subscript, 3, end subscript max
444 999 101010 131313 202020
According to the 1.5\cdot \text{IQR}1.5⋅IQR1, point, 5, dot, start text, I, Q, R, end text rule for outliers, how many high outliers are there in the data set?
Choose 1 answer:
c. probability that the mother in this sample had a premature baby given that the mother admitted to smoking
Probability that the mother in this sample had a premature baby given that the mother admitted to smoking is 50 percent.
What is probability?Likelihood is the part of science concerning mathematical depictions of how likely an occasion is to happen, or how likely it is that a suggestion is valid. The likelihood of an occasion is a number somewhere in the range of 0 and 1, where, generally talking, 0 demonstrates difficulty of the occasion and 1 shows conviction.
P (A) is the probability of an event “A”
n (A) is the number of favorable outcomes
n (S) is the total number of events in the sample space
The higher the likelihood of an occasion, the more probable it is that the occasion will happen. A straightforward model is the throwing of a fair coin. Since the coin is fair, the two results are both similarly likely; the likelihood of "heads" approaches the likelihood of "tails"; and since no different results are conceivable, the likelihood of by the same token "heads" or "tails" is 1/2.
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[tex]\sqrt{15}[/tex]
Answer:
3.87298335
Step-by-step explanation:
Answer:
3.872
Step-by-step explanation:
A card is selected to from a standard deck of 52 card what are the odds of selecting a red 9
The odds of selecting a red 9 is 1/26.
Probability of an event E is represented by P(E) can be defined as (the number of favorable outcomes) / (Total number of outcomes).
Given the total number of cards in a standard deck = 52
there can be only two red9 as one 9 from heart and one red from diamond.
So the number of outcome for red 9 =2
the probability of odds of selecting red 9 is [tex]\frac{2}{52}[/tex] which can be further simplified into [tex]\frac{1}{26}[/tex].
Therefore , The odds of selecting a red 9 is 1/26.
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Help me please! :)
And please explain how you got it
Answer:
-1.96312.. is a real, irrational number while √(-5) is imaginary. There is no value for a root of a negative number
Step-by-step explanation:
You should understand that numbers are naturally classified as real and imaginary. Under the real numbers, they are additionally classified into rational and irrational numbers. Under rational numbers, these possess fractions and integers. Irrational numbers are in decimal forms that cannot be converted to fractions. Thus, the difference between the two is that: -1.96312.. is a real, irrational number while √(-5) is imaginary. There is no value for a root of a negative number.
Combine like terms to find the perimeter of the figure.
Answer:
(29x +4) cm
Step-by-step explanation:
The perimeter of a figure is the sum of the lengths of all its sides.
Perimeter of figure
= 5x +5 +x +8x -3 +7x +2 +8x (sum up the lengths)
= 5x +x +8x +7x +8x +5 -3 +2 (group like terms together)
= (5 +1 +8 +7 +8)x +4
= (29x +4) cm
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MODELING REAL LIFE The average distance from Earth to the Sun is 92.95 million miles. The actual
distance varies from the average by up to 1.55 million miles. Write and solve an absolute value equation
to find the minimum and maximum distance from Earth to the Sun
The minimum and maximum distance from Earth to the Sun will be 90.7 million miles and 93.80 million miles.
How to calculate the value?From the information, The average distance from Earth to the Sun is 92.95 million miles. The actual
distance varies from the average by up to 1.55 million miles.
The minimum value will be:
= 92.25 - 1.55
= 90.7 million miles.
The maximum distance will be:
= 92.25 + 1.55
= 93.80 million miles.
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I got this answer wrong on my review, I didn't take 8th grade math so i'm kind of lost.
Answer: B
Step-by-step explanation:
I think it's B because if you solve the x and numbers by themselves then you get 4x-2
2x+3x = 5x
5x-1x= 4x
-5-2 = -7
-7+5= -2
4x-2
Estimate 65 square roots to the nearest tenth.
2x+3
7. Find each value if f(x)=x²-2x-8 and g(x)=-2x+1
(b) f(-3d)
(a) f(3)
(d) g(5)
(e) g(3x)
(e) f(2a-1)
(1) g(-4a+8)
Answer:
Step-by-step explanation:
a. f(-3d) = (-3d)^2 - 2(-3d) - 8 = 9d^2 + 6d - 8
b. f(3) = (3)^2 - 2(3) - 8 = 9 - 8 - 8 = 1 - 8 = -7
c. f(2a - 1) = (2a - 1)^2 - 2(2a - 1) - 8 = 4a^2 - 4a + 1 -4a + 2 - 8 = 4a^2 - 8a - 5
d. g(5)= (2(5)+3)/(5^2 -2(5) + 1) = (10 + 3)/(25 - 10 + 1)= 13/15+1= 13/16
e. g(3x)= (2(3x) + 3))/((3x)^2 - 2(3x) + 1))= (6x + 3)/(9x^2 - 6x + 1)
f. g(-4a + 8) = (2(-4a + 8)) + 3/(-4a + 8)^2 - 2(-4a +8) +1))
(-8a + 16 + 3)/(16a^2 - 32a + 64 + 8a - 16 + 1)
(-8a + 19)/(16a^2 - 24a + 49)
simply 7y2 - 5y + 9y - 5y2
Answer:
2y^2+4y
Step-by-step explanation:
7y^2-5y+9y-5y^2
=7y^2+4y-5y^2
=7y^2-5y^2+4y
=2y^2+4y
the sides of a triangle are of lengths 13, 14, and 15. the altitudes of the triangle meet at point h
The ratio HD:HA is 5/11 when the sides of a triangle are of lengths 13, 14, and 15.
What do you mean by heron's formula?When the lengths of all three sides are known, the geometry formula Heron's formula, which bears Hero of Alexandria's name, determines the area of a triangle. There is no need to first determine the angles or other distances in the triangle, unlike other triangle area formulas. Heron of Alexandria is credited with developing the Heron's formula, which determines the area of a triangle in terms of the lengths of its sides. If the side lengths are represented by the symbols a, b, and c: Area is equal to the square root of (a + b + c)/2, where s is half the perimeter.
By Heron's Formula, the area of this triangle is 84 Thus the height perpendicular to AB has a length of 11.2, and by the Pythagorean Theorem, AE and EB have lengths 6.6 and 8.4, respectively. These lengths tell us that C is at.
The slope of BC is (0-11.2)/(15-6.6)=-4/3, and the slope of AD is 3/4 by taking the negative reciprocal of -4/3. Therefore, the equation of line AD can best be represented by y=(3/4) x.
We next find the intersection of CE and AD . We automatically know the x -value; it is just 6.6 because CE is a straight line hitting (6.6,0). Therefore, the y -value is at (3/4)* 6.6=4.95. Therefore, the intersection between CE and AD is at (6.6,4.95) .
We also need to find the intersection between BC and AD . To do that, we know that the line of AD is represented as y=3/4x, and the slope of line BC is -4/3. We just need to find line BC 's y-intercept. So far, we have y=-4/3x+b, where b is a real y-intercept. We know that B is located at (15,0), so we plug that into the equation and yield b=20. Therefore, the intersection between the two lines is
(3/4)x=-(4/3)x+20
⇒9x=-16x+240
⇒25x=240
⇒x=9.6
Now y=(3/4)*x=(3/4)*9.6=7.2
⇒y=7.2
After that, we use the distance formula: HA has a length of
√(6.6-0)²+(4.95-0)²=√(1089/25)+(9801/400)
=√(1089*16+9801)/400
=√27225/400=√1089/16=33/4=8.25
and HD has a length of
√(9.6-6.6)²+(7.2-4.95)²=√(3)²+(36/5-99/20)²
=√(9)+(81/16)
=√225/16=15/4=3.75
So the ratio os HD:HA is
⇒3.75/8.25=15/33=5/11
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Find the coordinates of the midpoint of a segment with the given endpoints.
V(-2,5), Z(3,-17)
The coordinate of the midpoint of the segment with the given endpoints is ( 1/2, -6 ).
What is the midpoint of the segment with the given endpoint?The midpoint formular used in finding the midpoint of a segment is expressed as;
( [x₁+x₂]/2 , [y₁+y₂]/2 )
Given the data in the question;
Point V(-2,5)
x₁ = -2y₁ = 5Point Z(3,-17)
x₂ = 3y₂ = -17Plug these values into the equation above.
( [x₁+x₂]/2 , [y₁+y₂]/2 )
( [(-2) + 3]/2 , [5 + (-17)]/2 )
( 1/2 , -12/2 )
( 1/2, -6 )
The coordinate of the midpoint of the segment with the given endpoints is ( 1/2, -6 ).
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Help asap: use the number line to find the coordinate of p that represents the weighted average of the set of points such as point c has a weight of 3, and point e has a weight of 5
The coordinates weighted average is 6.
How is the weight average calculated?The whole query is as follows:
The weights of the coordinates 3 and 8 are 2 and 3, respectively. Additionally, we must determine the weighted average.
The parameters are as follows:
Three has a weight of two.
The weight of coordinate 8 is 3.
Next, the weight average is determined as follows:
Weight average is equal to the product of the weight and the coordinates.
We thus have:
Average weight: (3 * 2 + 8 * 3)/(2 + 3)
Assess the quotient.
Average weight = 6
Consequently, the coordinates' weighted average is 6
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Write the measurement with the indicated number of significant digits.
982. 1m^2
Using scientific notation, it is found that:
The number is written as follows: [tex]9.821 \times 10^2[/tex] m².The number has 4 significant digits, which are 9, 8, 2 and 1.What is scientific notation?A number in scientific notation is given by:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex].
For this problem, the number is given by:
982.1 m².
In scientific notation, the base has to be a number between 1 and 10(open interval at 10), hence the base has to be divided by 100.
To compensate for the division by 100, the number has to be multiplied by 100 somewhere, which happens when we add 2 to the exponent, as 10² = 100.
Hence:
The number is written as follows: [tex]9.821 \times 10^2[/tex] m².
The significant digits are all the digits that are not zero, and the zeros at the beginning or between other numbers, hence they are:
9, 8, 2 and 1.
Meaning that the number has 4 significant digits.
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what is the solution of 3z > 6
Answer:
Step-by-step explanation:
divide both sides by 3
3z>6
3z/3>6/3
z>2
Write an equation and solve: y decreased by 23 is 52.9
Answer:
y = 75.9
Step-by-step explanation:
Write an equation and solve: y decreased by 23 is 52.9
y - 23 = 52.9
y = 52.9 + 23
y = 75.9
------------------------
check
75.9 - 23 = 52.9
52.9 = 52.9
the answer is good
Complete the sentence.
21ft= ____yd.
21ft = 7yd or 21 feet is equivalent to 7 yards.
In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.
A conversion factor is a number used to change one set of units to another, either by multiplying or dividing.
The sentence states an equality between units of length: feet and yards.
From there, we can say that we are asked how many yards are there in 21 feet
Converting feet to inches, we must use the conversion
3 feet = 1 yard
21ft = 21/3 yards
21ft = 7yd
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James is making orange juice from concentrated frozen orange juice that he must mix with water. The concentrated juice is in 12 fluid ounce cartons. The ratio of orange juice concentrate to water is 12 fluid ounces to 36 fluid ounces. If James needs 4.5 gallon of orange juice, which is 576 fluid ounces, how many cartons of concentrated orange juice does he need?
Group of answer choices
In order to make 4.5 gallons of orange juice, she will need 12 cartons of concentrated orange juice.
The volume of concentrated orange juice is equal to 12 fluid-ounce cartons.Orange juice concentrate to water ratio = 12 fluid ounces to 36 fluid ouncesThe amount of orange juice required by James is 4.5 gallons (576 fluid ounces).So,
The orange juice concentrate to water ratio is 12:36.
Now, let's call 'x' the amount of concentrated orange juice in 4.5 gallons of orange juice and 'y' the amount of water in the 4.5 gallons of orange juice we have;
x + y = 4.5 (gallons) ...(1)x:y = 12:36 = 1:3∴ x/y = 1/33·x = y ...(2)We can conclude the following from equations (1) and (2):
x + y = 4.5x + 3·x = 4.5x = 4.5/4 = 1.125x = 1.125x = 1.125 gallons of concentrated orange juice in 4.5 gallons of orange juice:
y = 3 × x = 3 × 1.125 = 3.375y = 3.375y = 3.375, the amount of water in 4.5 gallons of orange juice.
As a result, we have;
4.5 gallons = 576 fluid ounces1.125 gallons = (576/4.5) × 1.125 = 144 fluid ouncesThe number of fluid ounces in a carton is 12 ounces.
The number of cartons in 144 fluid ounces = 144 fluidounces ÷ 12 fluidounces/carton = 12 cartonsIn 4.5 gallons of orange juice, x = 1.125 gallons = 144 fluidounces = 12 cartons of concentrated orange juice
x = 12 cartons of orange juice = the amount of concentrated orange juice she requires in 4.5 gallons of orange juiceThe amount of concentrated orange juice she requires in 4.5 gallons of orange juice, x = 12 cartons of orange juiceTherefore, in order to make 4.5 gallons of orange juice, she will need 12 cartons of concentrated orange juice.
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determine whether the points lie on a straight line. (a) a(2, 6, 1), b(3, 8, 0), c(1, 4, 2) yes, they do lie on a straight line. no, they do not. (b) d(0, −4, 4), e(1, −1, 3), f(3, 2, 2)
If the points lie on straight line then, the points should be collinear.
How do you know if the 3 points are on the line?We enter the values and check to see whether we receive a true statement, such as "10 Equals 10," to determine whether a point (x, y) is on the graph of a line. The point is not on the line if we obtain a result other than 6 = 4, as it does not meet the equation. Two lines will coincide if they have a same point and have the same slope. To put it another way, if A, B, and C are three points in the XY plane, they will all lie on a line, or three points will be collinear, but only if AB's slope and BC's slope are both equal.
(a) ab=kac
(3-2,8-6,0-1)=k(1-2,4-6,2-1)
⇒(1,2,-1)=k(-1,-2,1)=-k(1,2,-1) these are the points lie on stright line.
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Bobby bought movie tickets for 6 people
and popcorn for $19. If he spent a total of
$71.50, how much was each movie
ticket?
Help please
Answer:
$8.75
Step-by-step explanation:
y = 6x + 19
71.50 = 6x + 19 Subtract 19 from both sides of the equation
52.50 = 6x Divide both sides by 6
8.75 = x
At sunset a thermometer had a reading of 4'f during the night the temperature decreased 15'f after the decrease what is the total number of degrees that the temperature must change for the thermometer must read 0'f
If at sunset a thermometer had a reading of 4°F and during the night the temperature decreased by 15°F, then after the decrease the total number of degrees that the temperature must change for the thermometer to read 0°F is equal to 11°F.
The total number of degrees that the temperature must change for the thermometer to read 0°F can be determined by using subtraction.
Subtraction can be defined as an act of calculating the difference between numbers or values.
As the temperature decreased by 15°F during the night, the temperature after the decrease can be calculated as follows,
4°F - 15°F = -11°F
The total number of degrees the temperature must change for the thermometer to read 0°F can be calculated as follows,
-11°F + x = 0
x = 11°F
Hence, the temperature must increase by 11°F for the thermometer to read 0°F.
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Answer: 11’F
Step-by-step explanation:
4’F-15’F=-11
-11+11’F=0’F